

A277081


Irregular triangle read by rows: T(n,k) = number of size k subsets of S_n that remain unchanged under the operation of replacing a permutation with its inverse.


1



1, 1, 1, 1, 1, 2, 1, 1, 4, 7, 8, 7, 4, 1, 1, 10, 52, 190, 546, 1302, 2660, 4754, 7535, 10692, 13672, 15820, 16604, 15820, 13672, 10692, 7535, 4754, 2660, 1302, 546, 190, 52, 10, 1, 1, 26, 372, 3822, 31306, 216086, 1300420, 6981650, 33992275, 151945820
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,6


COMMENTS

T(n,k) is the number of size k subsets of S_n that remain unchanged under the operation of replacing a permutation with its inverse.


LINKS

Table of n, a(n) for n=0..48.


FORMULA

T(n,k) = Sum( C((n!  I(n))/2, i)*C(I(n), k  2*i) for i in [0..floor(k/2)]) where I(n) = A000085(n).


EXAMPLE

For n = 3 and k = 3 the subsets unchanged by inverse are {213,132,123}, {321,132,123}, {321,213,123}, {231,312,123}, {321,132,213}, {132,312,231},{213,312,231}, {321,231,312} hence T(3,3) = 8. (Here we are using the oneline notation for permutations, not the product of cycles form.)
Triangle starts:
1, 1;
1, 1;
1, 2, 1;
1, 4, 7, 8, 7, 4, 1;


CROSSREFS

Row lengths give A038507.
Cf. A000085.
Sequence in context: A265232 A011016 A096540 * A111569 A213786 A055130
Adjacent sequences: A277078 A277079 A277080 * A277082 A277083 A277084


KEYWORD

nonn,tabf,more


AUTHOR

Christian Bean, Sep 28 2016


STATUS

approved



